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Cambridge IGCSE Mathematics — 0580 Extended

Topic 9.5: Statistics — Charts and Diagrams

E9.4 is drawing and reading: dual and composite bar charts, pie charts, pictograms, stem-and-leaf diagrams and simple frequency distributions. Labels, a key, and a sensible scale are marks of their own.

Dual and composite bars

Dual (side-by-side) compares two groups. Composite (stacked) shows the split inside one group. Equal bar width, a gap between categories, labelled axes, and a legend.

Dual bar chart of four sports for Year 10 and Year 11
Leave a gap between sports. Same-category bars sit side by side.
Composite stacked bars versus dual bars of the same football data
Stacked answers ‘what share of Y10 is football?’. Dual answers ‘which year has more football?’.

Pie charts

\[ \text{angle} = \dfrac{\text{frequency}}{\text{total}} \times 360^\circ \]

Start at 12 o’clock and go clockwise. The four angles must sum to \(360^\circ\).

30 students: football 12, tennis 7, swimming 5, basketball 6. Find the pie angles.

Pie chart with sectors 144, 84, 60 and 72 degrees and the working panel
Football: \(12/30 \times 360 = 144^\circ\). Check: \(144+84+60+72=360\).

Pictograms

Every icon stands for the same number. A half-icon is allowed if the key says so. A missing key loses the mark.

Pictogram of four sports with each ball equal to two students
Football is 6 balls. Tennis is 3 balls and a half.

Stem-and-leaf

Leaves increase left to right. An unordered stem-and-leaf is incomplete. The key is compulsory and states the place value.

Method

  1. Split each value into a stem (left digits) and a leaf (last digit).
  2. Write stems in a column. Order the leaves on each row.
  3. Write a key, for example \(3\,|\,2\) means 32.
  4. Median, mode and range can then be read from the diagram.
Ordered stem-and-leaf of 15 marks with key 3 pipe 2 means 32
n = 15, so the median is the 8th value: 53. Mode = 45. Range = 75 − 32 = 43.
Back-to-back stem-and-leaf comparing Class A and Class B
One stem, two leaves. Class A sits higher; Class B has a tighter lower tail.

Paper 2 (non-calculator)

\(12/30 \times 360 = 144\) because \(12/30 = 2/5\) and \(2/5 \times 360 = 144\). Cancel before you multiply.

Try this

From the 15-mark stem-and-leaf, what is the range?

Show answer
Answer

  1. Largest 75, smallest 32.

    \[ 75 - 32 = 43 \]

Exam Traps

  • A stem-and-leaf without a key, or with unordered leaves, is not a finished diagram — examiners withhold the drawing mark.

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